# Properties

 Label 35378.k Number of curves 6 Conductor 35378 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35378.k1")

sage: E.isogeny_class()

## Elliptic curves in class 35378.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35378.k1 35378p6 [1, 0, 0, -48300183, -129206631191] [2] 2052864
35378.k2 35378p5 [1, 0, 0, -3016343, -2022438167] [2] 1026432
35378.k3 35378p4 [1, 0, 0, -628328, -157186184] [2] 684288
35378.k4 35378p2 [1, 0, 0, -186103, 30865575] [2] 228096
35378.k5 35378p1 [1, 0, 0, -9213, 688141] [2] 114048 $$\Gamma_0(N)$$-optimal
35378.k6 35378p3 [1, 0, 0, 79232, -14400576] [2] 342144

## Rank

sage: E.rank()

The elliptic curves in class 35378.k have rank $$0$$.

## Modular form 35378.2.a.k

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} - 2q^{6} + q^{8} + q^{9} - 2q^{12} - 4q^{13} + q^{16} - 6q^{17} + q^{18} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.